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The men are vying for a job that pays only $10,000 a year and comes with one vote on a seven-member city commission. . The city manager, Jimmy Morales, runs the city’s day-to-day operations.

During his tenure as mayor, Levine, a millionaire businessman who was elected in 2013, has gained favor with residents. For one, the city appointed a new police chief last year, and the department has remained largely free of negative headlines, a common occurrence previously.

Levine and city officials also successfully lobbied the state to expedite construction along Alton Road., and introduced a popular trolley service.

And the city installed anti-flooding pumps on low-lying West Avenue and in Sunset Harbour, where streets have remained dry during high tides.

But Levine’s first term wasn’t free of controversy. The mayor was involved with the political action committee Relentless for Progress, which raised about $1.4 million from city vendors, real-estate developers and lobbyists in what many perceived as a conflict of interest. Working with the chairman of the committee, term-limited Commissioner Jonah Wolfson, Levine solicited contributions for the now-defunct PAC, which intended to back candidates.

Levine told the Miami Herald he regrets his involvement: “I actually do. I think that in retrospect, understanding that the people felt that this is something they don’t like in Miami Beach, absolutely.”

Wieder said the PAC hurt the public’s trust in city hall: “I became sort of enraged about [the PAC]. I’d never run for political office before.”

He also believes the city, which increased its budget by $20 million this year, should rein in spending.

Wieder, who has served on the Historic Preservation Board for six years, applauds the pumps program but wants to make sure the city isn’t hurting Biscayne Bay. The water being pumped from city streets is flowing into Biscayne Bay.

He favors a Coral Gables-style approach to historic preservation, wanting to see the Historic Preservation Board review all requests for home demolitions — a popular position among the city’s most fervent preservationists.

He has said that he thinks the approach has worked well in the Gables, and homeowners would still have the ability to make a case for demolition.